Thanks to [1]}, the variety of 5-dimensional 2-step nilpotent algebras has only three irreducible components defined by
lllllll
\({\mathfrak {V}}_{4+1}\)   \(:\) 
\(e_1e_2=e_5\)  \(e_2e_1=\lambda e_5\)  \(e_3e_4=e_5\)\(e_4e_3=\mu e_5\)
\({\mathfrak {V}}_{3+2}\)  \( :\) 
\(e_1e_1 = e_4\)  \(e_1e_2 = \mu _1 e_5\)   \(e_1e_3 =\mu _2 e_5\) 
\(e_2e_1 = \mu _3 e_5\)   \(e_2e_2 = \mu _4 e_5\)
  \(e_2e_3 = \mu _5 e_5\)   \(e_3e_1 = \mu _6 e_5\)   2l\(e_3e_2 = \lambda e_4+ \mu _7 e_5\)    \(e_3e_3 = e_5\)
\({\mathfrak {V}}_{2+3}\)  \( :\) 
\(e_1e_1 = e_3 + \lambda e_5\)  \(e_1e_2 = e_3\)   \(e_2e_1 = e_4\)  \(e_2e_2 = e_5\)
Thanks to [2]}, [1]},
all 5-dimensional split Zinbiel algebras are in the orbit closure
of the families \({\mathfrak {V}}_{4+1}\)  and \({\mathfrak {V}}_{3+2},\) 
and the algebras
\([\mathfrak {Z}_1]^1_1, \, [\mathfrak {N}_1]^1_{01}, \, [\mathfrak {N}_1^{\mathbb {C}}]^1_{01}.\)
Let us give some useful degenerations for our proof.
|lcll|
\(\mathcal {Z}_{04}\)\(\rightarrow \)\(\mathcal {Z}_{01}\)  
\(E_1^t=e_1+\frac{2(3t^2-1)}{9t^2}e_4\)
3|l\(E_2^t=e_2+\frac{2(3t^2-1)}{9t^2}e_5\)  
\(E_3^t=-\frac{1}{3}e_2+\frac{3t^2}{3t^2-1}e_3\)
3|l\(E_4^t=-\frac{1}{9t}e_2+\frac{t}{3t^2-1}e_3+\frac{3t^2-1}{3t}e_4\)   \(E_5^t=e_5\)
\(\mathcal {Z}_{02}^{t-1}\)\(\rightarrow \)\(\mathcal {Z}_{03}\)  
\(E_1^t=e_1\)
3|l\(E_2^t=e_2\)  
\(E_3^t=e_3+\frac{1}{t}e_4\)
3|l\(E_4^t=e_4\)   \(E_5^t=e_5\)
\(\mathcal {Z}_{02}^{t+2}\)\(\rightarrow \)\(\mathcal {Z}_{04}\)  
\(E_1^t=e_1-\frac{2}{t}e_3\)
3|l\(E_2^t=e_2\)  
\(E_3^t=e_3\)
3|l\(E_4^t=\frac{t+2}{t}e_2+e_4\)   \(E_5^t=e_5\)
\(\mathcal {Z}_{22}\)  \(\rightarrow \)\(\mathcal {Z}_{07}\)  
\(E_1^t=e_1+\frac{\sqrt{4t^2-5}}{2(t^2-1)}e_3+\frac{2}{\sqrt{4t^2-5}}e_4\)
3|l\(E_2^t=\frac{t}{2(1-t^2)}e_1+\frac{t\sqrt{4t^2-5}}{2(t^2-1)}e_2\) 
\(E_3^t=\frac{t\sqrt{4t^2-5}}{2(t^2-1)}e_3-\frac{t}{2(t^2-1)}e_5\)
3|l\(E_4^t=\frac{2t}{\sqrt{4t^2-5}}e_4\)   \(E_5^t=\frac{t}{t^2-1}e_5\)
\(\mathcal {Z}_{22}\)  \(\rightarrow \)\(\mathcal {Z}_{08}\)  
\(E_1^t=e_1+\frac{\sqrt{t(4t^2-t-4)}}{2t(t^2-1)}e_3+2\sqrt{\frac{t}{4t^2-t-4}}e_4\)
3|l\(E_2^t=\frac{t}{2(1-t^2)}e_1+\frac{\sqrt{t(4t^2-t-4)}}{2(t^2-1)}e_2\) 
\(E_3^t=\frac{\sqrt{t(4t^2-t-4)}}{2(t^2-1)}e_3+\frac{t}{2(1-t^2)}e_5\)
3|l\(E_4^t=2t\sqrt{\frac{t}{4t^2-t-4}}e_4\)   \(E_5^t=\frac{t}{t^2-1}e_5\)
\(\mathcal {Z}_{10}^{-\frac{1}{t}}\)\(\rightarrow \)\(\mathcal {Z}_{09}\)  
\(E_1^t=e_1+e_2\)
3|l\(E_2^t=te_2\)   \(E_3^t=te_3\)
3|l\(E_4^t=e_3+te_4\)   \(E_5^t=te_5\)
\(\mathcal {Z}_{14}^{\frac{t^2-\alpha }{(\alpha -1)^2}}\)\(\rightarrow \)\(\mathcal {Z}_{10}^\alpha \)  
\(E_1^t=\frac{(\alpha -1)^2}{t}e_1+\frac{\alpha -1}{t}e_4\)
3|l\(E_2^t=e_2\)  
\(E_3^t=\frac{(\alpha -1)^2}{t}e_3\)
3|l\(E_4^t=(\alpha -1)e_4\)   \(E_5^t=\frac{(\alpha -1)^2}{t}e_5\)
\(\mathcal {Z}_{14}^{\frac{t+1}{4}}\)\(\rightarrow \)\(\mathcal {Z}_{11}\)  
\(E_1^t=\frac{4}{t}e_1-\frac{2}{t}e_4\)
3|l\(E_2^t=e_2\)  
\(E_3^t=\frac{4}{t}e_3\)
3|l\(E_4^t=-2e_4\)   \(E_5^t=\frac{4}{t}e_5\)
\(\mathcal {Z}_{22}\)\(\rightarrow \)\(\mathcal {Z}_{17}\)  
\(E_1^t=\frac{1}{t}e_1\)
3|l\(E_2^t=\frac{1}{2t^2}e_1+\frac{\sqrt{4t^2-1}}{2t^2}e_2\)   \(E_3^t=\frac{\sqrt{4t^2-1}}{2t^3}e_3-\frac{1}{2t^3}e_5\)
3|l\(E_4^t=-2\sqrt{4t^2-1}e_4\)   \(E_5^t=\frac{1}{t^3}e_5\)
\(\mathcal {Z}_{22}\)\(\rightarrow \)\(\mathcal {Z}_{20}\)  
\(E_1^t=e_1\)
3|l\(E_2^t=\frac{1}{2t}e_1+\frac{\sqrt{4t^2-1}}{2t}e_2\)  
\(E_3^t=\frac{\sqrt{4t^2-1}}{2t}e_3-\frac{1}{2t}e_5\)
3|l\(E_4^t=\frac{2}{\sqrt{4t^2-1}}e_4\)   \(E_5^t=\frac{1}{t}e_5\)
\(\mathcal {Z}_{24}\)\(\rightarrow \)\(\mathcal {Z}_{25}\)  
\(E_1^t=-(t+1)e_2-\frac{(t+1)(t+2)}{t}e_3-\frac{(t+1)}{t}e_4\)
3|l\(E_2^t=-te_1+e_2\)  
\(E_3^t=-t^2(t+1)e_3-(t+1)e_4+\frac{(t+1)^2}{t}e_5\)
3|l\(E_4^t=-t(t+1)e_3+(t+1)e_4\)   \(E_5^t=-(t+1)^2e_5\)
\(\mathcal {Z}_{27}\)\(\rightarrow \)\(\mathcal {Z}_{28}\)  
\(E_1^t=e_2\)
3|l\(E_2^t=te_1+e_3\)   \(E_3^t=te_4-e_5\)
3|l\(E_4^t=te_3\)   \(E_5^t=-te_5\)
\(\mathcal {Z}_{30}^{t}\)\(\rightarrow \)\(\mathcal {Z}_{31}\)  
\(E_1^t=-\frac{2t^2}{t+1}e_1+e_4\)
3|l\(E_2^t=e_2\)   \(E_3^t=e_3\)
3|l\(E_4^t=-\frac{2t^2}{t+1}e_4+2(t+1)e_5\)   \(E_5^t=-2t^2e_5\)
\(\mathcal {Z}_{35}\)\(\rightarrow \)\(\mathcal {Z}_{36}\)  
\(E_1^t=\sqrt{t}e_1-\frac{1}{3t}e_3+\frac{1}{\sqrt{t}}e_4\)
3|l\(E_2^t=\frac{1}{\sqrt{t}}e_1+e_2\)  
\(E_3^t=e_3\)
3|l\(E_4^t=\sqrt{t}e_4-\frac{2}{3t}e_5\)   \(E_5^t=e_5\)
\(\mathcal {Z}_{35}\)\(\rightarrow \)\(\mathcal {Z}_{37}\)  
\(E_1^t=\sqrt{t}e_1\)
3|l\(E_2^t=\frac{1}{\sqrt{t}}e_1+e_2\)   \(E_3^t=e_3\)
3|l\(E_4^t=\sqrt{t}e_4\)   \(E_5^t=e_5\)
\(\mathcal {Z}_{38}\)\(\rightarrow \)\(\mathcal {Z}_{39}\)  
\(E_1^t=e_1+\frac{3}{2\sqrt{t}}e_4\)
3|l\(E_2^t=e_2+\frac{9}{4t}e_5\)  
\(E_3^t=e_3\)
3|l\(E_4^t=-\frac{1}{2}e_3+\sqrt{t}e_4\)   \(E_5^t=e_5\)
\([\mathfrak {N}_1^{\mathbb {C}}]^2_{06}\)   \(\rightarrow \)   \([\mathfrak {N}_1^{\mathbb {C}}]^{2,\alpha }_{02}\)  
\(E_1^t=\frac{1}{\alpha -1}e_1+\frac{1}{(\alpha -1)^2}e_3\)
3|l\(E_2^t=\frac{1}{(\alpha -1)^2}e_2+\frac{1}{(\alpha -1)^3}e_4+\frac{\alpha }{(\alpha -1)^4}e_5\)   \(E_3^t=\frac{t}{(\alpha -1)^2}e_3\)
3|l\(E_4^t=\frac{1}{(\alpha -1)^3}e_4\)   \(E_5^t=\frac{t}{(\alpha -1)^4}e_5\)
\([\mathfrak {N}_1^{\mathbb {C}}]^{2,\frac{1}{2}}_{09}\)\(\rightarrow \)\([\mathfrak {N}_1^{\mathbb {C}}]^2_{07}\)  
\(E_1^t=te_1-te_3\)
3|l\(E_2^t=t^2e_2+t^2e_4-\frac{3t^2}{2}e_5\)  
\(E_3^t=t^2e_2+t^2e_3\)
3|l\(E_4^t=t^3e_4\)   \(E_5^t=\frac{t^{3}}{2}e_5\)
\([\mathfrak {N}_1^{\mathbb {C}}]^2_{06}\)  \(\rightarrow \)  \([\mathfrak {N}_1^{\mathbb {C}}]^{2,\alpha }_{09}\)   \(E_1^t=-\frac{2t^2}{(\alpha -1)(2\alpha -2t^2-1)}\left(e_1+\frac{1}{\alpha -1}e_3\right)\)
4|l|\(E_2^t=\frac{4t^4}{(\alpha -1)^2(2\alpha -2t^2-1)^{2}}\left(e_2+\frac{1}{\alpha -1}e_4+\frac{\alpha }{(\alpha -1)^2}e_5\right)\)
4|l|\(E_3^t=-\frac{2t^3}{(\alpha -1)^2(2\alpha -2t^2-1)}\left(\frac{1}{2\alpha -2t^2-1}e_2+e_3\right)\)
3|l\(E_4^t=-\frac{8t^6}{(\alpha -1)^3(2\alpha -2t^2-1)^{3}}e_4\)  
\(E_5^t=\frac{4t^5}{(\alpha -1)^3(2\alpha -2t^2-1)^{2}}\left(\frac{2}{2\alpha -2t^2-1} e_4+\frac{1}{\alpha -1}e_5\right)\)
\([\mathfrak {N}_1]^2_{02}\)\(\rightarrow \)\([\mathfrak {N}_1]^2_{01}\)   \(E_1^t=e_1+e_2\)
3|l\(E_2^t=te_2\)   \(E_3^t=te_3\)
3|l\(E_4^t=e_4\)   \(E_5^t=te_5\)
\([\mathfrak {N}_1]^2_{07}\)\(\rightarrow \)\([\mathfrak {N}_1]^2_{06}\)  
\(E_1^t=e_1+\frac{1}{t^2}e_2\)
3|l\(E_2^t=\frac{1}{t}e_2\)  
\(E_3^t=\frac{1}{t}e_3\)
3|l\(E_4^t=\frac{1}{t^2}e_4\)   \(E_5^t=\frac{1}{t^3}e_4+\frac{1}{t}e_5\)
\([\mathfrak {N}_1]^2_{08}\)\(\rightarrow \)\([\mathfrak {N}_1]^2_{07}\)  
\(E_1^t=\frac{1}{t}e_1+\frac{1}{t\sqrt{4t^2-1}}e_2\)
3|l\(E_2^t=\frac{2}{\sqrt{4t^2-1}}e_2\) 
 \(E_3^t=\frac{2}{t\sqrt{4t^2-1}}e_3-\frac{2}{t(4t^2-1)}e_4\)
3|l\(E_4^t=\frac{4}{t(4t^2-1)}e_4\)   \(E_5^t=\frac{2}{t^2(4t^2-1)}e_4+\frac{2}{t^2\sqrt{4t^2-1}}e_5\)
\([\mathfrak {N}_1]^2_{10}\)\(\rightarrow \)\([\mathfrak {N}_1]^2_{09}\)  
\(E_1^t=e_1+\frac{1}{t}e_2\)
3|l\(E_2^t=e_2-\frac{1}{t}e_3\)  
\(E_3^t=e_3-\frac{1}{t}e_5\)
3|l\(E_4^t=\frac{1}{t}e_4+\frac{1}{t^2}e_5\)   \(E_5^t=e_5\)
\([\mathfrak {N}_1]^2_{08}\)\(\rightarrow \)\([\mathfrak {N}_1]^2_{10}\)  
\(E_1^t=te_2-te_3\)
3|l\(E_2^t=-t^2e_1\)  
\(E_3^t=t^3e_3-t^3e_5\)
3|l\(E_4^t=t^3e_5\)   \(E_5^t=t^4e_4\)
\([\mathfrak {N}_1]^2_{08}\)\(\rightarrow \)\([\mathfrak {N}_1]^1_{01}\)  
\(E_1^t=te_1\)
3|l\(E_2^t=\sqrt{t}e_2\)  
\(E_3^t=\sqrt{t^3}e_3\)
3|l\(E_4^t=te_4\)   \(E_5^t=-e_4+\sqrt{t^3}e_5\)
\([\mathfrak {N}_1^\mathbb {C}]^2_{06}\)\(\rightarrow \)\([\mathfrak {N}_1^\mathbb {C}]^1_{01}\)  
\(E_1^t=\frac{1}{t-1}e_1\)
3|l\(E_2^t=\frac{1}{(t-1)^2}e_2\)  \(E_3^t=\frac{1}{t-1}e_3\)
3|l\(E_4^t=\frac{1}{(t-1)^3}e_4\)   \(E_5^t=-\frac{1}{t(t-1)^3}e_4+\frac{1}{t(t-1)^2}e_5\)
\(\mathcal {Z}_{40}\)\(\rightarrow \)\(\mathfrak {V}_{2+3}\)  
\(E_1^t=e_1-\frac{1}{t}e_2+\frac{3(2+9\lambda )}{8t^2}e_3-\frac{6(2+9\lambda )}{5t^3}e_4\)
3|l\(E_2^t=-\frac{3}{t}e_2\)  \(E_3^t=-\frac{3}{2t}e_3+\frac{9}{t^2}e_4-\frac{27(2+9\lambda )}{2t^3}e_5\)
3|l\(E_4^t=-\frac{3}{t}e_3+\frac{9}{t^2}e_4-\frac{9(2+9\lambda )}{t^3}e_5\)   \(E_5^t=\frac{27}{t^2}e_4\)
For the rest of degenerations, in case of \(E_1^t,\dots , E_n^t\)  is a parametric basis for \({\bf A}\rightarrow {\bf B},\)  it will be denote as
\({\bf A}\xrightarrow{} {\bf B}\) .
|lcl|lcl|
\(\mathcal {Z}_{09}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{06}\)
\(\mathcal {Z}_{13}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{12}\)
\(\mathcal {Z}_{14}^{\frac{1}{t^2}}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{13}\)
\(\mathcal {Z}_{16}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{15}\)
\(\mathcal {Z}_{22}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{16}\)
\(\mathcal {Z}_{22}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{18}\)
\(\mathcal {Z}_{22}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{19}\)
\(\mathcal {Z}_{22}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{21}\)
\(\mathcal {Z}_{25}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{26}\)
\(\mathcal {Z}_{28}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{29}\)
\(\mathcal {Z}_{34}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{32}\)
\(\mathcal {Z}_{34}\)   \( \xrightarrow{}\)   \(\mathcal {Z}_{33}\)
\([\mathfrak {N}_1^{\mathbb {C}}]^{2,\frac{1}{t}}_{02}\)   \( \xrightarrow{}\)   \([\mathfrak {N}_1^{\mathbb {C}}]^2_{01}\)
\([\mathfrak {N}_1^{\mathbb {C}}]^2_{06}\)   \( \xrightarrow{} \)  
\([\mathfrak {N}_1^{\mathbb {C}}]^2_{03}\)
\([\mathfrak {N}_1^{\mathbb {C}}]^2_{05}\)   \( \xrightarrow{} \)   \([\mathfrak {N}_1^{\mathbb {C}}]^2_{04}\)
\([\mathfrak {N}_1^{\mathbb {C}}]^2_{06}\)   \( \xrightarrow{} \)   \([\mathfrak {N}_1^{\mathbb {C}}]^2_{05}\)
\([\mathfrak {N}_1^{\mathbb {C}}]^{2,\frac{1}{t}}_{09}\)   \( \xrightarrow{} \)   \([\mathfrak {N}_1^{\mathbb {C}}]^2_{08}\)
\([\mathfrak {N}_1]^2_{07}\)   \( \xrightarrow{} \)   \([\mathfrak {N}_1]^2_{02}\)
\([\mathfrak {N}_1]^2_{04}\)   \( \xrightarrow{} \)   \([\mathfrak {N}_1]^2_{03}\)
\([\mathfrak {N}_1]^2_{08}\)   \( \xrightarrow{} \)   \([\mathfrak {N}_1]^2_{04}\)
\([\mathfrak {N}_1]^2_{06}\)   \( \xrightarrow{} \)   \([\mathfrak {N}_1]^2_{05}\)
\(\mathcal {Z}_{40}\)   \( \xrightarrow{} \)   \([\mathfrak {Z}_1]^1_{1}\)
The following dimensions of orbit closures are important for us:
llll
\(\dim \mathcal {O}({\mathfrak {V}}_{3+2})=24,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{22})=22,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{14}^\alpha )=21,\)  
\(\dim \mathcal {O}([\mathfrak {N}_1]^{2}_{08})=21,\)
\(\dim \mathcal {O}({\mathfrak {V}}_{4+1})=20,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{02}^\alpha )=20,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{30}^{\alpha })=20,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{05})=20,\)
\(\dim \mathcal {O}(\mathcal {Z}_{23})=20,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{24})=20,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{27})=20,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{35})=20,\)
\(\dim \mathcal {O}(\mathcal {Z}_{38})=20,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{40})=20,\)  
\(\dim \mathcal {O}([\mathfrak {N}_1^{\mathbb {C}}]^{2}_{06})=20,\)  
\(\dim \mathcal {O}(\mathcal {Z}_{34})=19.\)   
Let us, also, give the list of dimensions of the square of principal algebras:
|l|l|
dim \(A^2=2\)   \( \mathcal {Z}_{14}^\alpha , \, \mathcal {Z}_{02}^\alpha , \, \mathcal {Z}_{22}, {\mathfrak {V}}_{3+2}\)
dim \(A^2=3\)   \([\mathfrak {N}_1]^{2}_{08}, \,[\mathfrak {N}^{\mathbb {C}}_1]^{2}_{06}, \,\mathcal {Z}_{05}, \, \mathcal {Z}_{23}, \, \mathcal {Z}_{24}, \, \mathcal {Z}_{27}, \, \mathcal {Z}_{30}^{\alpha }, \, \mathcal {Z}_{34}, \, \mathcal {Z}_{35}, \, \mathcal {Z}_{38}\)
dim \(A^2=4\)   \(\mathcal {Z}_{40}\)
Hence, and taking into account the annihilator dimension of this algebras (see item \((2)\)  in the beginning of Section REF ),
\([\mathfrak {N}_1]^{2}_{08}, \, \mathcal {Z}_{05}, \, \mathcal {Z}_{22}, \, \mathcal {Z}_{23}, \, \mathcal {Z}_{24}, \, \mathcal {Z}_{27}, \, \mathcal {Z}_{30}^{\alpha }, \, \mathcal {Z}_{35}, \, \mathcal {Z}_{38}, \, \mathcal {Z}_{40}\)  and \({\mathfrak {V}}_{3+2}\)  give 11 irreducible components.
Below we have listed all necessary reasons for non-degenerations,
which imply that
\([\mathfrak {N}^{\mathbb {C}}_1]^{2}_{06},\mathcal {Z}_{02}^{\alpha }, \mathcal {Z}_{14}^{\alpha }, \mathcal {Z}_{34}\)  and \({\mathfrak {V}}_{4+1}\)  give another 5 irreducible components.
|rcl|l|
4|c|
Non-degenerations reasons
\([\mathfrak {N}_1]^{2}_{08}\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}[\mathfrak {N}^{\mathbb {C}}_1]^{2}_{06}\end{array} \) 
 \({\mathcal {R}}=\left\lbrace \begin{array}{l}A_1^2 \subseteq A_3, \, A_1A_4+A_4A_1=0, \\c_{11}^3=0, \, c_{22}^3=0, \, c_{12}^3=-c_{21}^3\end{array}\right.\)
\(\mathcal {Z}_{05}\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\end{array}\mathcal {Z}_{34}\)  \(& \) R=
{
l
A12 A3,   A1A2+A2A1 A4,   A4A3+A3A4=0,
c124=c214,   c123=c213=c223=0, 
2c245 = c425,   2c145 = c415
}\(\\\hline \)
\(\mathcal {Z}_{14}^{\alpha }\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\mathcal {Z}_{02}^{\alpha }, \\{\mathfrak {V}}_{4+1}\end{array} \) 
 \({\mathcal {R}}=\left\lbrace \begin{array}{l}A_1^2 \subseteq A_4, \, A_4A_1=0\\\end{array}\mbox{new base for }\mathcal {Z}_{14}^{\alpha }:f_1=e_1, f_2=e_2, f_3=e_4, f_4=e_3, f_5=e_5 \\\right.\) 
}\(\\\hline \)\(\mathcal {Z}_{22}\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\mathcal {Z}_{02}^{\alpha }, \\\mathcal {Z}_{14}^{\alpha }, \\{\mathfrak {V}}_{4+1}\end{array} \) 
 \({\mathcal {R}}=\left\lbrace \begin{array}{l}\end{array}\right.A_1^2 \subseteq A_4, \,A_1A_3+A_3A_1+A_2^2 \subseteq A_5,\,A_4A_1+A_1A_5=0, \\\mbox{new base for }\mathcal {Z}_{22}:f_1=e_1, f_2=e_2, f_3=e_4, f_4=e_3, f_5=e_5 \\\) 
}\(\\\hline \)
\(\mathcal {Z}_{23}\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\end{array}\mathcal {Z}_{34}\)  \(& \) R=
{
l
A12 A3,  
A1A3+A3A1 A5,  
A1A5+A4A1=0
}\(\\\hline \)\(\mathcal {Z}_{24}\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\end{array}\mathcal {Z}_{34}\)  \(& \) R=
{
l
A12 A3,  
A1A2 A4,
A1A3+A3A1 A5,  
A1A5+A5A1=0,
c224 c113= c124 c213,  
c235 c113= c135 c213,  
2 c224 c145= c124 c425,
c214 c145 + c124 c145 + c135 c213 = c124 c415,
c114 c145 c213 + c113 (c124 c145 + c135 c213) =c113 c124 c415
}\(\\\hline \)
\(\mathcal {Z}_{27}\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\end{array}\mathcal {Z}_{34}\)  \(& \) R=
{
A12 A3,   A3A1=0
l
}\(\\\)
\(\mathcal {Z}_{30}^{\alpha }\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\end{array}\mathcal {Z}_{34}\)  \(& \) R=
{
l
A12 A3,   A1A3+A3A1 A5,   A1A5+A5A1=0,
c123 = c213,  
c235 c425= c245 c325,
c315 c245 (c124 (c145)2 + 3 c113 c145 c235 - 2 c113 c135 c245) =
1r 2c145 (c124 c145 + 2 c113 c235) (c145 c235 - c135 c245)
}\(\\\hline \)
\(\mathcal {Z}_{35}\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\end{array}\mathcal {Z}_{34}\)  \(& \) R=
{
l
A12 A3,   A4A1+A32+A1A5=0,
c113 (c124 + c214)=2 c114 c123, 
c223(c124 + c214)= 2 c213 c224
}\(\\\hline \)\(\mathcal {Z}_{38}\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\end{array}\mathcal {Z}_{34}\)  \(& \) R=
{
l
A12 A3,   A1A2+A2A1 A4,
A22+A1A4+A4A1A5,   A1A5+A5A1=0,
c145 c114 +c113 c315 = 2c113 c135,  
2c124= c214
new base for Z38:
f1=e1, f2=e4, f3=e2, f4=e3, f5=e5

}\(\\\hline \)\(\mathcal {Z}_{40}\)  \(\lnot \rightarrow \) 
\( \begin{array}{l}\end{array}\mathcal {Z}_{34}\)  \(& \) R=
{
l
A12 A2,   A1A3+A3A1+A22 A4,
A2A3+A3A2 A5,   A5A1+A1A5=0,
4 c145 = c415,  
3c235 = 2 c325,  
3c134= c314,  
c213 = 2 c123
}\(\\\hline \)
